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The emergence of quasiparticles is a universal property in integrable systems. String-type quasiparticles, which are characterized by the string solutions of Bethe equations, play fundamental roles in the analysis of their physics. Through an investigation of the Bethe equations in the asymmetric simple exclusion process, we reveal the existence of string solutions in the presence of non-Hermiticity resulting from asymmetrical hopping. Because of the non-Hermiticity, the string solutions exhibit exotic properties such as the complexification of the center of string solutions and the delocalization of Bethe quantum numbers. In addition, we find the picture of string-type quasiparticles collapses in the strong-asymmetry regime. The collapse of string solutions characterizes the transition of eigenstates from bound states to scattering states.